connected surface

A solid is represented as a collection of connected surface elements, the boundary between solid and non-solid.

The final result is a connected surface that can be viewed as a spiralling parking garage with infinitely many levels extending both upward and downward.

Any connected surface with a three-dimensional group of isometries is a surface of constant curvature.

A closed (that is compact and without boundary) connected surface S of genus at least 1 is a classifying space for its fundamental group .

For a real number , let denote the unique simply connected surface (real 2-dimensional Riemannian manifold) with constant curvature .

The smooth and multiply connected surface will be mapped by the physics of a "large" particle as being singly connected and including geometrical singularities.

Claspers may also be interpreted algebraically, as a diagram calculus for the braided strict monoidal category Cob of oriented connected surfaces with connected boundary.

If is a map of closed connected surfaces such that is not injectiυe, then there exists a non contractible simple closed curve such that is homotopically trivial.

The bagpipe theorem states that every ω-bounded connected surface is the connected sum of a compact connected surface and a finite number of long pipes.

The complexity of a connected surface S, c(S), is defined to be ; the complexity of a disconnected surface is the sum of complexities of its components.

The Panel concludes that with the implementation of any necessary mitigation measures, the project is unlikely to result in significant adverse environmental effects on the basal aquifer groundwater regime or connected surface water bodies.

Microsoft and the NFL envision a sideline of the future with players reviewing in-game photos from different camera angles directly from the sideline and head coaches calling plays off connected Surface tablets instead of today's static paper products.

It was observed by Geroch, Jang, and Wald that if a closed, connected surface evolves smoothly under IMCF in a 3-manifold with nonnegative scalar curvature, then a certain geometric quantity associated to the surface, the Hawking mass, is non-decreasing under the flow.

Many results known for smooth surfaces and their geodesics, such as Birkhoff's method of constructing geodesics by his curve-shortening process or van Mangoldt and Hadamard's theorem that a simply connected surface of non-positive curvature is homeomorphic to the plane, are equally valid in this more general setting.